Abstract: Provided are a hollow shaft capable of increasing a static torsional strength and torsional fatigue strength of a small diameter portion (small diameter portion having a smooth outer peripheral surface) formed near a spline at an end portion of the hollow shaft, and capable of reducing cost, and a constant velocity universal joint using the hollow shaft. A hollow shaft (1) is molded by plastic working from a tubular blank, and subjected to quench hardening treatment. The quench hardening treatment includes carburizing and quenching treatment. The hollow shaft (1) includes a softened section (M) formed in a part of the hollow shaft (1) by local heating treatment after carrying out the carburizing and quenching treatment.